One-hop transmissions are the basis of multi-hop communications. In this section, the optimal transmission power, the optimal node density and the corresponding optimal expected ETD of one-hop transmissions are derived in order to optimize the energy efficiency in AWGN and Rayleigh block fading channels. Then, the results are extended to the case of multi-hop transmissions.
5.3.1 Optimization of one-hop transmission
The optimization of the energy efficiency can be abstracted as a nonlinear programming (NP) problem:
Minimize : EDRb (5.19)
Subject to : Pt> 0, ρ > 0.
The sequential quadratic programming (SQP) method algorithm in [67] is adopted to solve the optimization problem in this works. Fig. 5.5 shows the optimization results in AWGN and Rayleigh block fading channels concerning the different ψ, where the
0.1pi 0.2pi 0.3pi 0.4pi 0.5pi 0.6pi 0.7pi 0.8pi 0.9pi 4.5 5 5.5 6 6.5x 10 −5
ψ
Optimal mean EDRb (mJ/bit/m)
Rayleigh block fading channel AWGN channel
Figure 5.5: Optimal EDRb in AWGN and Rayleigh block fading with respect to ψ.
parameters used are given in Table 2.1. The corresponding optimal parameters are provided in Fig. 5.6.
The results in Fig.5.5show that the EDRb increases energy monotonically, namely, the energy efficiency decreases, in these two kinds of channels with the increase of ψ. Meanwhile, it should be noticed that the EDRb in Rayleigh block fading channel is smaller than that in AWGN channel for the same ψ, that is to say, the energy effi- ciency is improved in Rayleigh block fading channel by opportunistic communications compared with the results in [87]. Moreover, the optimal dtx in Rayleigh block fad-
ing channel is greater than that in AWGN channel as shown in Fig. 5.6 (c). This result indicates that the opportunistic communication scheme can exploit the benefit of fading.
EDRb increases monotonically with the augment of ψ in two kinds of channels.
This result suggests that relay candidates should be selected which are close to the linear path between the source and the destination to improve the energy efficiency. In addition, using directional antennas will prove to be more efficient because the antenna gain in (2.11) increases with the reduction of the aperture angle.
Another point should be noted that the links are still unreliable even when there are multiple receivers as shown in Fig. 5.6 (d), which indicates that the trad-off be- tween the multiuser diversity introduced by the opportunistic communications and the temporal diversity introduced inherently by retransmissions exits in the opportunistic communication.
72 Minimum energy transmission
0.1pi 0.2pi 0.3pi 0.4pi 0.5pi 0.6pi 0.7pi 0.8pi 0.9pi 14 16 18 20 22 24 26 ψ
Optimal transmission power (mW)
Rayleigh block fading channel AWGN channel
(a) Optimal transmission power P t0
0.1pi 0.2pi 0.3pi 0.4pi 0.5pi 0.6pi 0.7pi 0.8pi 0.9pi 0 0.2 0.4 0.6 0.8 1x 10 −3 ψ
Optimal node density (node/m
2)
Rayleigh block fading channel AWGN channel
(b) Optimal node density ρ0
0.1pi 0.2pi 0.3pi 0.4pi 0.5pi 0.6pi 0.7pi 0.8pi 0.9pi 90 100 110 120 130 140 150 160 ψ
Optimal expected ETD (m)
Rayleigh block fading channel AWGN channel
(c) Optimal expected ETD d0tx
0.1pi 0.2pi 0.3pi 0.4pi 0.5pi 0.6pi 0.7pi 0.8pi 0.9pi 70 72 74 76 78 80 82 ψ
Optimal link probabity (%)
Rayleigh block fading channel AWGN channel
(d) Optimal link probability
0.1pi 0.2pi 0.3pi 0.4pi 0.5pi 0.6pi 0.7pi 0.8pi 0.9pi 1.25 1.3 1.35 1.4 1.45 ψ
Optimal mean delay (units) Rayleigh block fading channel AWGN channel
(e) Optimal mean delay D0
Figure 5.6: Corresponding optimal parameters for the example in Fig. 5.5.
5.3.2 Analyses of multi-hop transmission
On the basis of the results of one-hop transmission, we can extend the corresponding results to multi-hop transmissions in a scenario of one source and one destination in a fixed distance d >> dtx.
According to dtx, the average number of hops is: Nhop=
d d0tx
, (5.20)
where d0tx is the optimal expected ETD for one-hop transmission. Then the average
end-to-end energy consumption Ee2e and delay De2e are computed respectively by: Ee2e= Nhop· E1hop(P t0, ρ0). (5.21)
De2e= Nhop· D0. (5.22)
5.4
Simulations
In the simulations, dtx is evaluated in a square area A with the surface area SA =
500× 500m2 in AWGN and Rayleigh block fading channels. The nodes are uniquely deployed according to a Poisson distribution with the density 0.0003π/ψ for each ψ to keep the Piso constant. BPSK is adopted in the simulations and the bit rate is 1Mbps.
In each simulation, the source node S sends a packet of 2560 bits with a transmission power of 10mW . The nodes in the communication sector ofS try to receive the packet. In each simulation, the recorded ETD corresponds to the node receiving successfully the packet and being the closest to the destination. The simulations are run 10000 times for each ψ.
The differences between simulation results and theoretical results obtained by (5.13) are smaller than 0.5% as shown in Fig.5.4, which proofs the correctness of (5.13).
5.5
Summary
Firstly, we propose an analytical framework of opportunistic communication, which provides a method for optimizing the different opportunistic schemes. Meanwhile, the energy efficiency of opportunistic communications with respect to different forwarding areas is studied in regard to the optional transmission power and the optional node density in AWGN and Rayleigh block fading channels. The analyses show that oppor- tunistic communications are more efficient in Rayleigh block fading channel than that in AWGN channel from an energy point of view. Further, the mechanism of selecting the forwarding candidates which locate around the linear path between the source and the destination is more energy efficient than that of selecting all neighbor nodes.
6
Energy-Delay Trade-off of Opportunistic
Communications
6.1
Introduction
The energy efficiency performance of opportunistic communications is analyzed in Chapter 5, in which all neighbors in its communication area of a source act as for- warding candidates. The results of Chapter 5 show the importance of selection of relay candidates to the energy efficiency. Therefore, considering the optimal number of forwarding relays, we evaluate the maximal efficiency that can be achieved with such opportunistic routing in this chapter.
Concerning this question, we propose in this chapter to calculate the lower bound of the energy-delay trade-off for opportunistic communications under a hard end-to- end reliability constraint. To compute this bound, we consider the size of candidate cluster and the transmission power as variables of the optimization problem. As stated previously, we focus on the two following questions: what is the best set of relay candidates and what is the performance of the optimized set of candidates?
With regard to the routing policy, we assume that for a given cluster, only the candidate closest to the destination is selected to forward the packet. Such a strategy obviously relies on the assumption that each node has the full knowledge of the position of itself and the destination. Once a node has a packet to send, it appends the locations of itself and the intended relay cluster to the packet, then broadcasts it. The relay
76 Models and metric
candidates which successfully receive the packet (solid nodes in Fig. 4.1) assess their own priorities of acting as relay, based on how close they are to the destination. The best
relay which is the closest to the destination relays the packet, as shown in Fig. 4.1. In contrast with the the aforementioned schemes, this scheme utilizes an optimized candidate cluster, instead of all the active neighbors, to receive the packet for the purpose of saving energy and taking advantage of the spatial diversity.
The main contributions of this chapter are:
• A general framework for evaluating the maximal efficiency of the opportunistic
routing principle is provided. Energy and delay are compromised under an end- to-end reliability constraint.
• The Pareto front of energy-latency trade-off is derived for different scenarios. A
close-form expression of energy-delay tradeoff when the number of relay candi- dates is fixed, and an algorithm to find the optimal number of relay candidates is proposed. The simulations results verify the correctness of this lower bound in a 2-dimension Poisson distributed network. The numerical analyses show that opportunistic routing is inefficient in AWGN channel, while efficient in Rayleigh block fading channel on the condition of a small cluster size.
• The lower bound of energy efficiency is derived and its corresponding maximal
delay is obtained.
• An opportunistic relay selection mechanism is proposed to minimize energy con-
sumption under a delay constraint.
The rest of this chapter is organized as follows: Section 6.2 describes the utilized models and metrics in this chapter. In Section 6.3, the lower bounds of energy-delay tradeoff and energy efficiency are obtained for one-hop transmissions. Then, this result is extended to the scenario of multi-hop transmissions in section 6.4, and the gain of opportunistic communication on energy efficiency is analyzed in this section. The opti- mization of the physical and protocol layer parameters on the lower bound is presented in Section 6.5. In Section 6.6, the theoretical results about lower bound of energy- delay tradeoff are verified and a new opportunistic protocol is introduced. Section 6.7
discusses the effects of these results and gives some conclusions.
6.2
Models and metric
In this section, we introduce the energy and delay models, the realistic link model and the metric EDRb and DDR used in this work. The cluster size of relay candidates is given by NR.
6.2.1 System model
In this thesis, the nodes in a network are assumed to be independently and randomly distributed according to a random Poisson process of density ρ, which is defined in (3.1).
We consider the case of a source node S forwarding a packet to a sink/destination node D. ni is one ofS’s neighbors which is closer to D than S.
In addition, each ni is associated with a pair, (pli, di), where pli is the link proba-
bility between ni and S which is defined in (2.10) and di is the effective transmission
distance which is calculated by:
di = Dist(S, D)− Dist(ni, D) (6.1)
where Dist(i, D) and Dist(ni, D) are the Euclidian distance between S and D and
between ni andS respectively.
S has the knowledge of the location of itself, all neighbors and D, and the link
probability pli. S selects the forwarding candidate set among all neighbors according
to some priority on the basis of these information about neighbors. Let F denote the forwarding candidate set, which includes all the nodes involved in the local collaborative forwarding and the number of nodes inF is NR.
6.2.2 Energy consumption model
According to the models of energy consumption in Chapter5, the energy consumption per bit is:
Eb= Ep Nb
= Ec+ K1· Pt (6.2)
where Ep is defined in (5.14), Ptis the transmission power. Here, K1· Ptstands for the
radio emission energy and Ec denotes the circuit energy per node, which are obtained
by: Ec=(1 + τack)· ( (NR+ 1)· Tstart· Pstart Nb + (1 + τhead) ( NR PrxElec RbRcode + PtxElec RbRcode )) , (6.3) K1=(1 + τack)(1 + τhead)· βamp RbRcode , (6.4)
where τack and τhead are defined in (2.5) and (2.9) respectively, and the related param-
78 Models and metric
6.2.3 Realistic unreliable link models
According to the opportunistic relaying principle, the successful transmission means that at least one node receives the packet correctly. Therefore, for NR forwarding
nodes whose sequence is based on the protocol priority, the probability of a successful transmission is: ps= N R ∑ i=1 pli i∏−1 j=1 (1− plj), (6.5)
where pl is the link probability between two nodes and is defined in (2.10).
In this part, retransmissions and acknowledgement mechanism also are adopted in this thesis to ensure a reliable transmission. The mean of transmission Ntx is:
Ntx= ∞
∑
n=1
n· psdata· psack· (1 − psdata· psack)(n−1)
= 1
psdata· psack
, (6.6)
where n is the number of transmissions, psdata and psack are the successful transmission
probability of DATA packet and ACK packet respectively calculated by (6.5).
In the acknowledgment process, as described in Chapter 2 we can assume that
psack = 1, in another words, only one ACK packet is sent with high probability of
success to the source of the message. Therefore, Ntx can be approximated by: Ntx≈
1
ps
, (6.7)
where ps replaces for psdata for simplification.
6.2.4 mean Energy Distance Ratio per bit (EDRb)
According to the definition of EDRb, we have:
EDRb = Eb(Pt)· Ntx dtx
, (6.8)
where dtx is the expected transmission distance for opportunistic communication . It
should be noticed that this metric integrates all factors of physical and link layers. Then, we focus on dtx [85]: dtx= 1 ps · NR ∑ i=0 di· pl(di, Pt) i∏−1 j=1 (1− pl(dj, Pt)). (6.9)
Substituting (6.7), (6.2) and (6.9) into (6.8), we obtain: EDRb = ∑N R Ec + K1Pt i=0di· pl(di, Pt) ∏i−1 j=1(1− pl(dj, Pt)) . (6.10)
6.2.5 Delay Distance Ratio (DDR)
The delay of a packet to be transmitted over one hop, Dhop, is defined in (2.23) as the
sum of three delay components. The first component is the queuing delay during which a packet waits for being transmitted, Tqueue. The second component is the transmission
delay that is equal to Nb
RbRcode. The third component is TACK. Note that we neglect
the propagation delay because the transmission distance between two nodes is usually short in multi-hop networks.
Furthermore, a reliable one-hop transmission will suffer from the delay caused by retransmissions. According to (6.7), the mean delay of a reliable one-hop transmission is:
Dhop= DhopNtx. (6.11)
DDR is adopted as the metric of delay also. It is defined in opportunistic commu-
nications as: DDR = DhopNtx dtx = ∑N R Dhop i=0di· pl(di, Pt) ∏i−1 j=1(1− pl(dj, Pt)) . (6.12)